Exponent Rules Math 2

Vocabulary When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.

What is an Integer Exponent? An integer exponent means that you multiply the base by itself that many times (the integer). For example x4 = x ● x ● x ● x 26 = 2 ● 2 ● 2 ● 2 ● 2 ● 2 = 64

Rational Exponent If the power of the exponent raised to a number in the form p/q where q is not 0, then the exponent is a rational exponent. Examples:

Radical Expression An radical expression is an expression that has a square root, cube root, etc. A radical expression is also called the nth root of am Examples:

Equivalent Forms Equivalent forms are expressions that are equivalent. Examples:

The Invisible Exponent When an expression does not have a visible exponent its exponent is understood to be 1.

Exponent Rule #1 When multiplying two expressions with the same base you add their exponents. For example

Exponent Rule #1 Try it on your own:

Exponent Rule #2 When dividing two expressions with the same base you subtract their exponents. For example

Exponent Rule #2 Try it on your own:

Exponent Rule #3 When raising a power to a power you multiply the exponents For example

Exponent Rule #3 Try it on your own

Note When using this rule the exponent can not be brought in the parenthesis if there is addition or subtraction You would have to use FOIL in these cases

Exponent Rule #4 When a product is raised to a power, each piece is raised to the power For example

Exponent Rule #4 Try it on your own

Note This rule is for products only. When using this rule the exponent can not be brought in the parenthesis if there is addition or subtraction You would have to use FOIL in these cases

Exponent Rule #5 When a quotient is raised to a power, both the numerator and denominator are raised to the power For example

Exponent Rule #5 Try it on your own

Zero Exponent When anything, except 0, is raised to the zero power it is 1. For example ( if a ≠ 0) ( if x ≠ 0)

Zero Exponent Try it on your own ( if a ≠ 0) ( if h ≠ 0)

Negative Exponents If b ≠ 0, then For example

Negative Exponents If b ≠ 0, then Try it on your own:

Negative Exponents The negative exponent basically flips the part with the negative exponent to the other half of the fraction.

Math Manners For a problem to be completely simplified there should not be any negative exponents

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